integral from 1 to 3 of ((3x^2+4x+1)/x)

Lösung

\int_{1}^{3} (\frac{3 x ^{2} + 4 x + 1}{x}) d x

ln (3) + 20

Dezimale

21.09861 \dots

Schritte zur Lösung

\int_{1}^{3} \frac{3 x ^{2} + 4 x + 1}{x} d x

Multipliziere aus

\frac{3 x ^{2} + 4 x + 1}{x} : 3 x + 4 + \frac{1}{x}

= \int_{1}^{3} 3 x + 4 + \frac{1}{x} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{3} 3 x d x + \int_{1}^{3} 4 d x + \int_{1}^{3} \frac{1}{x} d x

\int_{1}^{3} 3 x d x = 12

\int_{1}^{3} 4 d x = 8

\int_{1}^{3} \frac{1}{x} d x = ln (3)

= 12 + 8 + ln (3)

Vereinfache

= ln (3) + 20

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